I had a similar problem and couldn't find any solution for the desktop version, in particular, for Ubuntu 22.04 (jammy). However, this should also work for the pgadmin4-web:

sudo curl https://www.pgadmin.org/static/packages_pgadmin_org.pub | sudo apt-key add
sudo sh -c 'echo "deb https://ftp.postgresql.org/pub/pgadmin/pgadmin4/snapshots/2022-05-05/apt/jammy pgadmin4 main" > /etc/apt/sources.list.d/pgadmin4.list && apt update'
sudo apt install pgadmin4-web

(Don't forget to run sudo /usr/pgadmin4/bin/setup-web.sh after that)

For the desktop version just install pgadmin4-desktop instead of pgadmin4-web:

sudo apt install pgadmin4-desktop

Also, please note that this is a temporary solution (May 2022), until the devs release the final pgadmin4 version for jammy. Once it's out, you would just need to update the repository.

Hope this helps.

For pgAdmin 4 v4.21 on Ubuntu, according to the download page:

Install dependencies, create a virtual environment, download, install & configure

Using Python2.x

sudo apt-get install virtualenv python-pip libpq-dev python-dev

cd
virtualenv pgadmin4
cd pgadmin4
source bin/activate

pip install https://ftp.postgresql.org/pub/pgadmin/pgadmin4/v4.21/pip/pgadmin4-4.21-py2.py3-none-any.whl

Using Python3.6 (Preferred to avoid encoding related issues)

sudo apt-get install virtualenv python3-pip libpq-dev python3-dev

cd
virtualenv -p python3 pgadmin4
cd pgadmin4
source bin/activate

pip3 install https://ftp.postgresql.org/pub/pgadmin/pgadmin4/v4.21/pip/pgadmin4-4.21-py2.py3-none-any.whl

Configure

Override default paths and set it to single-user mode in the local configuration file:

nano lib/python2.7/site-packages/pgadmin4/config_local.py

For Python3.x:

nano lib/python3.6/site-packages/pgadmin4/config_local.py

Write:

import os
DATA_DIR = os.path.realpath(os.path.expanduser(u'~/.pgadmin/'))
LOG_FILE = os.path.join(DATA_DIR, 'pgadmin4.log')
SQLITE_PATH = os.path.join(DATA_DIR, 'pgadmin4.db')
SESSION_DB_PATH = os.path.join(DATA_DIR, 'sessions')
STORAGE_DIR = os.path.join(DATA_DIR, 'storage')
SERVER_MODE = False

Run

python lib/python2.7/site-packages/pgadmin4/pgAdmin4.py

For Python3.x:

python3 lib/python3.6/site-packages/pgadmin4/pgAdmin4.py

Access

Access at http://localhost:5050

Exit

Exit with Ctrl-C

Run again

cd ~/pgadmin4
source bin/activate
python lib/python2.7/site-packages/pgadmin4/pgAdmin4.py

For Python3.6

#!/bin/bash
cd ~/pgadmin4
source bin/activate
python3 lib/python3.6/site-packages/pgadmin4/pgAdmin4.py

Make a shortcut

touch ~/pgadmin4/pgadmin4
chmod +x ~/pgadmin4/pgadmin4
nano ~/pgadmin4/pgadmin4

Write:

#!/bin/bash
cd ~/pgadmin4
source bin/activate
python lib/python2.7/site-packages/pgadmin4/pgAdmin4.py

For Python3.6

#!/bin/bash
cd ~/pgadmin4
source bin/activate
python3 lib/python3.6/site-packages/pgadmin4/pgAdmin4.py

Now you can just run it with a simpler command:

~/pgadmin4/pgadmin4

Python3 users

Replace [x] in Python3.6 with your respective version.

Conflict with pgAdmin 3 configuration

pgAdmin 4 will not start in the environment where pgAdmin 3 was previously installed and used because of incompatible configuration in the .pgadmin directory. The simplest solution is to either clear that directory or tweak config_local.py to point to a clean new .pgadmin4 directory.